Pope
Lv 7
Pope asked in Science & MathematicsMathematics · 10 years ago

What is the radius of these spheres?

Begin with one red sphere of unit radius. On its surface evenly distribute twenty congruent blue spheres. Each of the blue spheres is externally tangent to the red sphere and to exactly three of the other blue spheres. What is the radius of a blue sphere?

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  • Anonymous
    10 years ago
    Favourite answer

    As the centers of the twenty spheres are at the vertices of a regular dodecahedron, their radii r satisfy the equation

    1+r = r/2 (√¯15 + √¯3)

    the answer is

    r = 2/(√¯15 + √¯3 - 2) = 0.554779765

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